Presenting a two-fluid models of accretion disks in active galactic nuclei (AGNs) that aim to address the long-standing problem of Toomre instability in AGN outskirts. In the spirit of earlier works by Sirko & Goodman and others, we argue that Toomre instability is eventually self-regulated via feedback produced by fragmentation and its aftermath. Unlike past semianalytic models, which (i) adopt local prescriptions to connect star formation rates to heat feedback, and (ii) assume that AGN disks self-regulate via star-formation (with Toomre parameter Q_T= 1), we find that feedback processes are both temporally and spatially nonlocal. The accumulation of many stellar-mass black holes embedded in AGN gas eventually displaces radiation, winds, and supernovae from massive stars as the dominant feedback source. The nonlocality of feedback heating, in combination with the need for heat to efficiently mix throughout the gas, gives rise to AGN solutions that can have Q_T ≫ 1 and no ongoing star formation. We find self-consistent solutions in much of the parameter space of AGN mass and accretion rate. These solutions harbor large populations of embedded compact objects that may grow in mass by factors of a few over the AGN lifetime, including into the lower and upper mass gaps. These feedback-dominated AGN disks differ significantly in structure from commonly used 1D disk models, which has broad implications for gravitational-wave-source formation inside AGNs.